PolySheaf Neural Networks for Railway Passenger Prediction

This project applies Polynomial Sheaf Neural Networks (PolySheafNNs) to the problem of railway passenger flow prediction. Railway networks are naturally graph-structured — stations are nodes, rail segments are edges — making them an ideal testbed for geometric deep learning methods that exploit topology.

Background: Sheaf Neural Networks

Standard GNNs assign a single feature vector to each node and aggregate over neighbours. Sheaf Neural Networks generalise this by assigning sheaves — structured spaces of signals — to nodes and edges, with restriction maps specifying how signals on edges relate to signals on their endpoint nodes. This richer structure allows the network to model more complex inter-node relationships than scalar or vector aggregation.

Polynomial sheaves parameterise restriction maps as low-degree polynomials, providing a tractable and expressive family for learning.

Application

• Graph: railway network where nodes are stations and edges are rail links.
• Signals: passenger counts per station per time window.
• Task: multi-step ahead forecasting of passenger volumes.
• Evaluation: compared against standard GCN and LSTM baselines on a real railway dataset.

Technology

Implemented in Python with PyTorch Geometric. Experiments run in Jupyter Notebooks with reproducible training loops and evaluation metrics (MAE, RMSE).